Wait for leaves and flowers.

Hi WRF, I think your two large trees are some type of ash like Fantex, Shamel or Majestic Beauty. They lose their leaves for a brief period in January and leaf out again in late February. Ash trees need lots of water and often struggle in our urban landscapes so be sure your irrigation system (drip/hose, etc.) is delivering enough. Ash trees with a 15 foot diameter canopy will need about 300 gallons of water once every 10 days in summer and once every 3 weeks in winter. If yours are larger, they'll need more of course. It looks as though they've both had numerous branches removed previously so don't prune them again for a while. Remember that the more green leaves that remain on a tree the more food (sugars) are being made. The tree uses the sugars to grow and if you prune too much you starve the tree. Don't let anyone talk you into thinning your ash trees, they look fine. Mexican Fan Palms have tall, slender trunks and the petioles (stems) of the leaves have teeth along the edges. They can be pretty messy around pools with falling flowers and seeds. Plus when they get as tall as yours you'll need to hire someone to prune and or skin it (remove brown leaf bases) which can be expensive. If you like the palm look around your pool, opt for the smaller palms like Pygmy Date, Windmill or Mediterranean Fan. You could even look at larger palms like Mexican Blue or Pindo which grow slowly. Here's a link to a list of plants suitable for pool landscapes. Here is a link that might be useful: Plants for Poolsides

Thank you all for the help identifying this. I'm thinking I'm going to try to get rid of it - would garden experts agree that this is one I shouldn't feel bad about getting rid of? FataMorgana- when you said the early leaves don't always look like mature leaves.... Any chance that my giant collection of "little spreaders" that is popping up with on pairs of opposed leaves is just a pre-woody-vine version of this? Thank you all again for the help- one down five hundred to go! :-)

Mulberries are one of these love/hate things. By your driveway, definitely no (because of the mess). Way at the back of a fairly large property, definitely yes (wildlife food). Looks like yours is interfering with the fence and causing a problem.